Put the garlic onto a cutting board and sprinkle it with about 1/2 teaspoon salt. Using the side of a large knife, slowly mash the garlic into a paste. Put the garlic paste into a small bowl and blend in 1/2 cup olive oil, parsley, and thyme leaves. Pour half the mixture over the chicken and season it with salt and pepper. Set the chicken aside to marinate while you prepare the other ingredients for grilling.
Heat the grill to medium high. Drizzle half the remaining marinade into the mushrooms and half onto the cut side of the radicchios. Season both with salt and pepper and place them on the grill over indirect heat. Grill until the mushrooms and radicchio are soft, about 10 to 15 minutes; set them aside to cool while you cook the chicken
Put the chicken on the grill and cook for about 15 to 20 minutes per side, or until cooked through and juices run clear. Set aside until cool enough to handle.
To serve, cut the chicken into pieces, cut the mushrooms into quarters, and cut the radicchio into wedges. Gently toss everything together with some fresh watercress and an extra drizzle of olive oil.